Competitions

# ATM

In some country in circulation there are notes of certain denominations. National Bank wants the cash machine to give out any requested amount with a minimum number of banknotes, considering that the amount of banknotes of each denomination is unlimited.

Help the National Bank to solve this problem.

#### Input

First line contains the number of banknotes denominations in circulation n (n100). Second line contains n different positive integers x1, x2, ..., xn not greater than 106 - the banknotes denominations. Third line contains the sum s (s106) that you want to give.

#### Output

Print in the first line the minimal number of summands (or -1 if such representation does not exist). In the second line print these summands in any order.

Time limit 1 second
Memory limit 128 MiB
Input example #1
5
1 3 7 12 32
40

Output example #1
3
32 7 1